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# If |x–1|<4, so:

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Intern
Joined: 26 Feb 2017
Posts: 30
Location: Brazil
GMAT 1: 610 Q45 V28
GPA: 3.11
If |x–1|<4, so:  [#permalink]

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24 Oct 2017, 04:10
2
29
00:00

Difficulty:

95% (hard)

Question Stats:

26% (01:16) correct 74% (01:19) wrong based on 665 sessions

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If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above
Math Expert
Joined: 02 Sep 2009
Posts: 50044
Re: If |x–1|<4, so:  [#permalink]

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24 Oct 2017, 04:13
2
7
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above

$$|x–1|<4$$;

$$-4<x-1<4$$;

$$-3<x<5$$.

Any x from that range will be more than -4.

P.S. What is the source of this question?
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Intern
Joined: 26 Feb 2017
Posts: 30
Location: Brazil
GMAT 1: 610 Q45 V28
GPA: 3.11
Re: If |x–1|<4, so:  [#permalink]

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24 Oct 2017, 04:24
Bunuel wrote:
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above

$$|x–1|<4$$;

$$-4<x-1<4$$;

$$-3<x<5$$.

Any x from that range will be more than -4.

P.S. What is the source of this question?

Bunnel,

First of all, thank you very much.

The source of this questions is a bank of questions that I received from a friend, whose his teacher gave to him.

I have huge doubts on inequalities topics.

As you explained above any value X>-4 can satisfy this.

What is the best approach to deal with this kind of questions? I solved -3<x<5, but I could not figure out, X>-4 because -3>-4 and do not satisfy the inequality.

I have the same doubt on this question, below...

https://gmatclub.com/forum/if-z-2-4z-5- ... l#p1949237
Math Expert
Joined: 02 Sep 2009
Posts: 50044
If |x–1|<4, so:  [#permalink]

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24 Oct 2017, 04:27
1
2
vitorpteixeira wrote:
Bunuel wrote:
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above

$$|x–1|<4$$;

$$-4<x-1<4$$;

$$-3<x<5$$.

Any x from that range will be more than -4.

P.S. What is the source of this question?

Bunnel,

First of all, thank you very much.

The source of this questions is a bank of questions that I received from a friend, whose his teacher gave to him.

I have huge doubts on inequalities topics.

As you explained above any value X>-4 can satisfy this.

What is the best approach to deal with this kind of questions? I solved -3<x<5, but I could not figure out, X>-4 because -3>-4 and do not satisfy the inequality.

I have the same doubt on this question, below...

https://gmatclub.com/forum/if-z-2-4z-5- ... l#p1949237

It's the other way around. We know that $$-3<x<5$$. Any x from that range satisfy x > -4.

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Re: If |x–1|<4, so:  [#permalink]

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25 Oct 2017, 10:40
Bunuel wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above

$$|x–1|<4$$;

$$-4<x-1<4$$;

$$-3<x<5$$.

Any x from that range will be more than -4.

P.S. What is the source of this question?[/quote]

Hi, Bunuel
Just wanted to ask that since in this question it is not mentioned that x is an integer, by the range x>-4 it will include values greater than -3 also (say -3.8) but our range is from -3 to 5 so isnt this wrong????
Math Expert
Joined: 02 Sep 2009
Posts: 50044
Re: If |x–1|<4, so:  [#permalink]

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25 Oct 2017, 10:51
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Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If |x–1|<4, so:  [#permalink]

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26 Oct 2017, 15:47
1
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above

We can solve the inequality when (x - 1) is positive and when it is negative.

When (x - 1) is positive:

x - 1 < 4

x < 5

When (x - 1) is negative:

-x + 1 < 4

-x < 3

x > -3

-3 < x < 5

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Manager
Joined: 15 Feb 2017
Posts: 77
If |x–1|<4, so:  [#permalink]

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26 Oct 2017, 17:53
3
IMO Option D is the right answer.
|x-1|<4 means
-4<x-1<4
-3<x<5
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Joined: 05 Dec 2016
Posts: 246
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: If |x–1|<4, so:  [#permalink]

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27 Oct 2017, 05:01
It's a tricky question, I think I've encountered a sort of this one in OG2017.
Key to solve it is to find the range from the answer choices that covers all possible values of x,here it is answer choice D.
Intern
Joined: 24 Nov 2016
Posts: 32
Re: If |x–1|<4, so:  [#permalink]

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27 Oct 2017, 11:03
1
I can't understand why x>-4 is the correct answer.

Since we have -3<x<5 , -3 is out of the range and in x> -4 -3 is included in the number line.

Besides that, X>-4 we can have x=10, as an exemple, wich is not true since x<5.

Can someone help me with this points?

tks
Intern
Joined: 07 Jul 2017
Posts: 10
Re: If |x–1|<4, so:  [#permalink]

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01 Nov 2017, 08:13
Bunuel wrote:
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above

$$|x–1|<4$$;

$$-4<x-1<4$$;

$$-3<x<5$$.

Any x from that range will be more than -4.

P.S. What is the source of this question?

Hi Bunuel, thanks for the explanation. I tend to approach this questions in the wrong way, trying to find an answer choice that matches with the range found through the inequalities. For instance, in this case I was looking for -3<x<5 (or something more restrictive, such as -2 < x < -5), which led me to pick answer E.

Given your explanation, I understand that I should look for that condition that holds for every x in the range...but I still have a huge doubt.
You say it is (D) x > -4 because any X from that range will be more than -4. Following your logic, wouldn't also B) x ≤ 4 be true? Our range is -3<x<5, which means that every x will be less or equal to 4.

Is there something I am not getting right?

Your help is super appreciated
Math Expert
Joined: 02 Sep 2009
Posts: 50044
Re: If |x–1|<4, so:  [#permalink]

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01 Nov 2017, 09:53
1
delid wrote:
Bunuel wrote:
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above

$$|x–1|<4$$;

$$-4<x-1<4$$;

$$-3<x<5$$.

Any x from that range will be more than -4.

P.S. What is the source of this question?

Hi Bunuel, thanks for the explanation. I tend to approach this questions in the wrong way, trying to find an answer choice that matches with the range found through the inequalities. For instance, in this case I was looking for -3<x<5 (or something more restrictive, such as -2 < x < -5), which led me to pick answer E.

Given your explanation, I understand that I should look for that condition that holds for every x in the range...but I still have a huge doubt.
You say it is (D) x > -4 because any X from that range will be more than -4. Following your logic, wouldn't also B) x ≤ 4 be true? Our range is -3<x<5, which means that every x will be less or equal to 4.

Is there something I am not getting right?

Your help is super appreciated

For $$-3<x<5$$, (B) x ≤ 4 won't always be true. For example, x could be 4.5 (4.5 IS between -3 and 5) and in this case B is not true.
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Re: If |x–1|<4, so:  [#permalink]

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04 Nov 2017, 04:02
|x–1|<4

−3<x<5

Any x from that range will be more than -4.

Math Expert
Joined: 02 Sep 2009
Posts: 50044
Re: If |x–1|<4, so:  [#permalink]

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14 Jan 2018, 23:12
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above

Check other similar questions from Trickiest Inequality Questions Type: Confusing Ranges (part of our Special Questions Directory).
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Re: If |x–1|<4, so:  [#permalink]

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26 Mar 2018, 15:50
Wouldn't this question be better off as a "which of the following must be true" question? Does the actual test do stuff like this?
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# If |x–1|<4, so:

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